If $X=48,Y=15$, then the value of $k$ such that $X(\mathrm{mod}Y)=(X+kY)(\mathrm{mod}Y)$ is:

1. A
   no such $k$ exists
2. B
   $k$ is any positive integer
3. C
   $k$ is any negative integer
4. D
   $k$ is any integer